Nope you can only use private courier while sending but when they send it back to you they WILL ONLY use Canada Post. Cic tells you that in their website to put a Canada Post Xpresspost standard size envelope enclosed inside the larger envelope which ypu ill use to send ypur passport. They will use the standard sized envelope to send it back to you( they say that on their website). In my case I send the Canada Post Xpresspost envelope and my passport enclosed in a UPS larger envelope. The reason being that since I knew Canada Post is facing delays, It would be faster if the delay is only from one instance rather than both sending nd receiving. Know that CIC WILL NOT USE a return envelope from a private courier to return your passport and in that case will send you the passport by regular un trackable Canada post mail.